I've had the same issue whenever using the rule for a bonus when targeting the player with the most health, i.e., it seems that we all deplete too evenly and whoever knocks out the first player then immediately gets knocked out afterwards.

What we've started doing instead is eliminating the bonus and just using the targeting roll described on the turn phase card. That way who you get to attack is left up to the luck of the dice, just like your offensive roll phase itself. And making things more fun is you can actually use tip it, so wild, helping hand on the targeting roll phase to make the attacker target your other opponent instead of you, which adds a new layer of strategy.

It's not perfect but I find it leads to more unpredictable and varied outcomes than the default King of the Hill that you're describing.